Gaussian Spatial Linear Model of Soybean Yield Using Bootstrap Methods

Abstract

This study aims to quantify the uncertainties associated to the parameters of a Gaussian spatial linear model (GSLM) and the assumption of normality residuals in the modeling of the spatial dependence of the soybean yield as a function of soil chemical attributes. The spatial bootstrap methods were used to determine the point and interval estimators associated with the model parameters. Hypothesis tests were carried out on the significance of the model parameters and the quantile-quantile probability plot was elaborated to verify the data normality. The uncertainties associated to the parameters of the spatial dependence structure were quantified and the potassium content, phosphorus content and soil pH covariates were significant to explain the soybean yield mean. These covariates were used in the elaboration of a new model, which provided the elaboration of a contour map of soybean yield. Analysis of the quantile-quantile plot indicated that soybean yield data follow a normal probability distribution.

Spatial-temporal Analysis of Soybean Productivity Using Geostatistical Methods

“…The circular regions close to the sampling points as explained by Menezes et al (2016), represent the phenomenon known as the "bull eyes effect." This phenomenon was also observed by Dalposso et al (2018) and occurs when the geostatistical model has a range close to the minimum distance between sample points. Because the models used to create the maps above had a range of 65.25 m (Table 1) and 77.16 m (Table 2), respectively, and the shortest distance between points was 49.1 m, the presence of circular regions is justified.…”

Geostatistical Modeling of Soybean Yield and Soil Chemical Attributes Using Spatial Bootstrap

“…Given that little geostatistical data are available, there is uncertainty about the obtained values and, consequently, the shape of the semivariogram is debatable (Olea & Pardo-Igúzquiza, 2011). This topic has been gaining prominence because of the need to obtain realistic results during geostatistical modeling (Sari et al, 2015;Dalposso et al, 2018).…”

“…However, few studies to date used the bootstrap method to analyze spatial data. This method was also used to monitor arsenic pollution in Portugal (García-Soidán et al, 2014), to obtain robust empirical estimators of variance for spatial autocorrelation (Villoria & Liu, 2018), and to model the spatial dependence of soybean yield using soil chemical attributes as covariates (Dalposso et al, 2018).…”